Free Maths Calculator

Trigonometry Calculator

SOHCAHTOA without the guesswork: say which sides you know relative to the angle, and the calculator picks sin, cos or tan for you, explains why, and finds the missing side or angle. The labelling step comes first every time, because choosing the right ratio is the whole battle.

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    Worked Example

    In a right-angled triangle the hypotenuse is 8 cm and one angle is 30°. Find the side opposite the angle.

    1. The sides in play are the opposite and the hypotenuse, so use sin (SOH)
    2. sin(30°) = 0.5
    3. opposite = hypotenuse × sin(30°):8 × 0.5 = 4

    Answer: 4 cm

    Try These Yourself

    The opposite is 3 cm and the adjacent is 4 cm. Find the angle.Show answerHide answer

    Answer: 36.87°

    tan θ = 3 ÷ 4 = 0.75, then θ = tan⁻¹(0.75).

    The angle is 45° and the adjacent is 6 cm. Find the opposite.Show answerHide answer

    Answer: 6 cm

    tan(45°) = 1, so the opposite equals the adjacent.

    The opposite is 5 cm and the hypotenuse is 10 cm. Find the angle.Show answerHide answer

    Answer: 30°

    sin θ = 5 ÷ 10 = 0.5, and sin⁻¹(0.5) = 30°.